1235 LearnersLast updated on June 4th, 2025
Summary statistics
As the name suggests, summary statistics is the summary of the data set. As the data is simplified to a simpler form it helps the reader to understand and analyze the data easier. In this topic, we will learn more about summary statistics in detail.
What Is Summary Statistics?
The summary of the data in a statistical form is known as the summary statistics. It is a part of descriptive statistics that summarizes the given data. The collection, organization, summaries, and presentation of data are known as descriptive statistics.
In statistics, we use different measures to analyse and describe datasets. To measure central tendency, we use mean, median, and mode. In summary statistics, to measure how to spread out the data point, we measure it using range, variance, standard deviation, mean absolute deviation, and so on.
How to Compare Summary Statistics for Two or More Sets of Quantitative Data
For comparing summary statistics for two or more sets of data, we use the measures of center and measures of variability. Follow these steps to compare two or more sets of quantitative data
Identify the measures of the center
To measure the center means finding the value which is centered. To find it the methods we use are mean, median, and mode.
How the comparison is done:
- The average of the dataset is the mean. If the mean of the two or more datasets is the same it means the overall values of the datasets are the same. If the mean is different, then one dataset has higher values.
- If the median is lower than the mean, then the dataset can be right-skewed. If the median is higher than the mean, then the dataset can be left-skewed.
Identify the measures of variability
The measures of variability are how the data is spread out. The common measures are range, IQR, variance, and standard deviation.
How the comparison is done:
- If the data set has a higher standard deviation means more variation
- If the IQR is smaller then the values are more consistent
What is the equation for Summary Statistics?
Summary statistics are used to describe the characteristics of a data set. Now let’s learn a few equations used for summary statistics:
- Mean = Sum of the data points/total number of values
- Range = maximum value - minimum value
- Standard deviation (sd) = (xi - x̄)2/N - 1, where n is the number of observations, xi is the observations, and x is the mean
- Weighted mean (xw) = i = 1N wi × xii = 1N wi, where N is the number of observations, xi is the observation, wi is the weights
- Weighted standard deviation (sdw) = i = 1N wi (xi - xw)2(N' - 1)N' i = 1N wi, where N is the number of observations, Xi is the observations, x̄w is the weighted mean, N’ is the number of non-zero weights.
Real-life applications of Summary Statistics
We learned a lot about summary statistics. Now, let’s see how we use summary statistics in real life to analyse and interpret data.
- In educational institutions, to analyse students performance we use median and mode.
- To analyse the sales and revenue analysis, we use mean sales and standard deviation.
- Statistics are used in sports, we used to compare the players' performances
- The summary statistics such as range and variance is used to track the mean rainfall
Common Mistakes and How to Avoid Them in Summary Statistics
When working on summary statistics, students tend to repeat the same mistakes. So, let’s learn a few common mistakes and how to avoid them in Summary Statistics.
Mistake 1
Confusing mean and median
Students often confuse mean and median, so to avoid this mistake, they need to understand the concept. The mean is the dataset's average, and the median is the middle of the data set when arranging the numbers in ascending order.
Solved Examples of Summary Statistics
Problem 1
Sarah recorded her math test scores for the last five tests: 85, 90, 78, 92, and 88. What is her average test score?
The average score is 86.6
Explanation
To find the average, we use the formula;
Average = sum of the terms/number of terms
Here, the sum of the scores: 85 + 90 + 78 + 92 + 88 = 433
Number of terms = 5
Average = 433 / 5 = 86.6
Problem 2
A teacher recorded the heights (in cm) of 7 students: 150, 160, 158, 155, 162, 157, and 159. What is the median height?
The median height is 158 cm
Explanation
To find the median, we arrange the height in ascending order
150, 155, 157, 158, 159, 160, 162
Here, the middle value is 4, so the median is 158 cm
Problem 3
The following are the ages of students in a classroom: 12, 13, 12, 14, 15, 13, 12, 13, 16. Find the mode of the data.
Here, the mode data is 12 and 13
Explanation
To find the mode, let’s count the frequency of each age
Age
Frequency
12
3
13
3
14
1
15
1
16
1
Here, 12 and 13 have more frequency as there are two values, so the dataset is bimodal.
Problem 4
The daily temperatures (in °C) for a week were 25, 28, 30, 32, 29, 26, and 31. Find the range of the temperatures.
The range of the temperature is 7 °C
Explanation
Sorting the data in ascending order: 25, 26, 28, 29, 30, 32
Identifying the maximum and minimum temperatures
The maximum temperature is 32 °C
The minimum temperature is 25°C
The range = maximum temperature - minimum temperature
= 32 - 25 = 7 °C
Problem 5
A company recorded the weekly sales of a product over 5 weeks: 50, 60, 55, 65, and 70 units. Find the variance
Here, the variance is 50
Explanation
Calculate the mean of the given data
That is (50+ 60 + 55 + 65 + 70) / 5 = 300 / 5 = 60
Calculating each number’s deviation from the mean
(50 - 60)2 = (-10)2 = 100
(60 - 60)2 = (0)2 = 0
(55 - 60)2 = (-5)2 = 25
(65 - 60)2 = (5)2 = 25
(70 - 60)2 = (10)2 = 100
Calculating the variance that is
(100 + 0 + 25 + 25 + 100) / 5 = 250/5 = 50
FAQs on Summary Statistics
1.What are summary statistics?
2.What is the most common summary statistic?
3.What is the difference between mean, median, and mode?
4.How do you calculate the range of a dataset?
5.How do you calculate the mean?
6.How can children in United States use numbers in everyday life to understand Summary statistics?
7.What are some fun ways kids in United States can practice Summary statistics with numbers?
8.What role do numbers and Summary statistics play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Summary statistics skills?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
